Stochastic modeling of multidimensional particle properties with parametric copulas for the investigation of microstructure effects on the fractionation of fine particle system

在这个项目中，在战略规划项目2045的第一个资助期开发的数学分析和建模技术将应用于战略规划项目2045内的合作伙伴所调查的粒子系统的图像数据和测量。此外，还进一步发展了量化分离成功率的方法，以及多维颗粒特征与分离相关物理参数之间的关系。此外，还开发了一个体视学预测模型，用于通过粒子系统从2D切片中表征3D粒子。特别是，将处理以下任务。在第一个资助期开发的用于从CT图像数据中提取颗粒、用于对颗粒特征的多变量分布进行参数建模、用于从CT数据表征复合颗粒中的材料以及用于量化分离成功的方法被应用于更多的颗粒系统，并在必要时进行了修改。为此，将从CT数据中自动提取颗粒以及随后对颗粒的多变量特征分布进行建模的工作流程应用于分离过程应用之前和之后的颗粒系统。这减少了(困难的)直接比较CT图像数据为比较进料和产品的颗粒特性分布。随后，确定了分离成功的指标，如纯度和得率，以分析和比较分离方法的质量。另一个项目目标是利用随机三维颗粒模型，即通过生成描述颗粒形状和内部结构的“数字孪生”，来量化颗粒特性与分离成功之间的关系。此外，这些模型允许生成范围广泛的具有不同特征分布的虚拟但真实的粒子。这些虚拟颗粒将通过颗粒数据库提供给SPP 2045的伙伴小组，以便伙伴可以将它们用作沉积和流动过程的数值模拟的输入。通过将模拟结果与进料颗粒特性的多变量分布相关联，将确定颗粒特性与分离成功之间的关系。此外，开发了一个体视学预测模型，该模型通过粒子系统从2D切片(例如通过扫描电子显微镜测量获得)确定3D粒子特征的多变量分布。为此，将上述随机(单)粒子模型扩展为空间分散粒子系统的模型。通过生成大量的虚拟3D粒子系统，训练神经网络，它可以从所考虑的粒子系统的2D切片中刻画3D粒子。

In this project, the mathematical analysis and modeling techniques developed in the first funding period of the SPP 2045 will be applied on image data and measurements of particle systems which are investigated by the partners within SPP 2045. In addition, the methods are further developed, which quantify the separation success and the relationship between multidimensional particle characteristics and separation-relevant physical parameters. Furthermore, a stereological prediction model is developed to characterize 3D particles from 2D sections through the particle systems. In particular, the following tasks will be addressed. The methods developed in the first funding period for extracting particles from CT image data, for parametric modeling of multivariate distributions of particle characteristics, for characterizing the materials within composite-particles from CT data, and for quantifying the separation success, are applied to further particle systems and modified if necessary. For this purpose, the workflow, consisting of the automated extraction of particles from CT data and the subsequent modeling of multivariate feature distributions of the particles, is applied to particle systems before and after the application of separation processes. This reduces the (difficult) direct comparison of CT image data to the comparison of distributions of particle characteristics of the feed material and the product. Subsequently, measures for the separation success, such as purity and yield, are determined to analyze and compare the quality of the separation methods. Another project goal is to quantify the relationship between particle properties and separation success using stochastic 3D particle models, i.e., by generating "digital twins" which describe the shape and internal structure of the particles. Furthermore, these models allow the generation of a wide range of virtual but realistic particles with different feature distributions. These virtual particles will be made available to the partner groups of SPP 2045 via a particle database, such that the partners can use them as input for numerical simulations of sedimentation and flow processes. By correlating the simulation results with multivariate distributions of characteristics of the feed particles, relationships between particle properties and separation success will be determined. In addition, a stereological prediction model is developed, which determines multivariate distributions of characteristics of 3D particles from 2D slices (gained e.g. by SEM measurements) through the particle system. For this purpose, the above-mentioned stochastic (single) particle models are extended to a model for spatially dispersed particle systems. By generating a large number of virtual 3D particle systems neural networks are trained, which can characterize the 3D particles from 2D sections of the considered particle system.